Application of Improved Deep Auto-Encoder Network in Rolling Bearing Fault Diagnosis

Since the effectiveness of extracting fault features is not high under traditional bearing fault diagnosis method, a bearing fault diagnosis method based on Deep Auto-encoder Network (DAEN) optimized by Cloud Adaptive Particle Swarm Optimization (CAPSO) was proposed. On the basis of analyzing CAPSO and DAEN, the CAPSO-DAEN fault diagnosis model is built. The model uses the randomness and stability of CAPSO algorithm to optimize the connection weight of DAEN, to reduce the constraints on the weights and extract fault features adaptively. Finally, efficient and accurate fault diagnosis can be implemented with the Softmax classifier. The results of test show that the proposed method has higher diagnostic accuracy and more stable diagnosis results than those based on the DAEN, Support Vector Machine (SVM) and the Back Propagation algorithm (BP) under appropriate parameters.

Subspace clustering via graph auto-encoder network for unknown encrypted traffc recognition

The traffic encryption brings new challenges to the identification of unknown encrypted traffc.Currently,machine learning is the most commonly used encrypted traffic recognization technology,but this method relies on expensive prior label information.Therefore,we propose a subspace clustering via graph auto-encoder network(SCGAE)to recognize unknown applications without prior label information.The SCGAE adopts a graph encoder-decoder structure,which can comprehensively utilize the feature and structure information to extract discriminative embedding representation.Additionally,the self-supervised module is introduced,which use the clustering labels acts as a supervisor to guide the learning of the graph encoder-decoder module.Finally,we obtain the self-expression coefficient matrix through the self-expression module and map it to the subspace for clustering.The results show that SCGAE has better performance than all benchmark models in unknown encrypted traffic recognization.

End-to-End Auto-Encoder System for Deep Residual Shrinkage Network for AWGN Channels

With the rapid development of deep learning methods, the data-driven approach has shown powerful advantages over the model-driven one. In this paper, we propose an end-to-end autoencoder communication system based on Deep Residual Shrinkage Networks (DRSNs), where neural networks (DNNs) are used to implement the coding, decoding, modulation and demodulation functions of the communication system. Our proposed autoencoder communication system can better reduce the signal noise by adding an “attention mechanism” and “soft thresholding” modules and has better performance at various signal-to-noise ratios (SNR). Also, we have shown through comparative experiments that the system can operate at moderate block lengths and support different throughputs. It has been shown to work efficiently in the AWGN channel. Simulation results show that our model has a higher Bit-Error-Rate (BER) gain and greatly improved decoding performance compared to conventional modulation and classical autoencoder systems at various signal-to-noise ratios.

Screening biomarkers for spinal cord injury using weighted gene co-expression network analysis and machine learning

Immune changes and inflammatory responses have been identified as central events in the pathological process of spinal co rd injury.They can greatly affect nerve regeneration and functional recovery.However,there is still limited understanding of the peripheral immune inflammato ry response in spinal cord inju ry.In this study.we obtained microRNA expression profiles from the peripheral blood of patients with spinal co rd injury using high-throughput sequencing.We also obtained the mRNA expression profile of spinal cord injury patients from the Gene Expression Omnibus(GEO)database(GSE151371).We identified 54 differentially expressed microRNAs and 1656 diffe rentially expressed genes using bioinformatics approaches.Functional enrichment analysis revealed that various common immune and inflammation-related signaling pathways,such as neutrophil extracellular trap formation pathway,T cell receptor signaling pathway,and nuclear factor-κB signal pathway,we re abnormally activated or inhibited in spinal cord inju ry patient samples.We applied an integrated strategy that combines weighted gene co-expression network analysis,LASSO logistic regression,and SVM-RFE algorithm and identified three biomarke rs associated with spinal cord injury:ANO10,BST1,and ZFP36L2.We verified the expression levels and diagnostic perfo rmance of these three genes in the original training dataset and clinical samples through the receiver operating characteristic curve.Quantitative polymerase chain reaction results showed that ANO20 and BST1 mRNA levels were increased and ZFP36L2 mRNA was decreased in the peripheral blood of spinal cord injury patients.We also constructed a small RNA-mRNA interaction network using Cytoscape.Additionally,we evaluated the proportion of 22 types of immune cells in the peripheral blood of spinal co rd injury patients using the CIBERSORT tool.The proportions of naive B cells,plasma cells,monocytes,and neutrophils were increased while the proportions of memory B cells,CD8^(+)T cells,resting natural killer cells,resting dendritic cells,and eosinophils were markedly decreased in spinal cord injury patients increased compared with healthy subjects,and ANO10,BST1 and ZFP26L2we re closely related to the proportion of certain immune cell types.The findings from this study provide new directions for the development of treatment strategies related to immune inflammation in spinal co rd inju ry and suggest that ANO10,BST2,and ZFP36L2 are potential biomarkers for spinal cord injury.The study was registe red in the Chinese Clinical Trial Registry(registration No.ChiCTR2200066985,December 12,2022).

An Efficient Encryption and Compression of Sensed IoT Medical Images Using Auto-Encoder

Healthcare systems nowadays depend on IoT sensors for sending data over the internet as a common practice.Encryption ofmedical images is very important to secure patient information.Encrypting these images consumes a lot of time onedge computing;therefore,theuse of anauto-encoder for compressionbefore encodingwill solve such a problem.In this paper,we use an auto-encoder to compress amedical image before encryption,and an encryption output(vector)is sent out over the network.On the other hand,a decoder was used to reproduce the original image back after the vector was received and decrypted.Two convolutional neural networks were conducted to evaluate our proposed approach:The first one is the auto-encoder,which is utilized to compress and encrypt the images,and the other assesses the classification accuracy of the image after decryption and decoding.Different hyperparameters of the encoder were tested,followed by the classification of the image to verify that no critical information was lost,to test the encryption and encoding resolution.In this approach,sixteen hyperparameter permutations are utilized,but this research discusses three main cases in detail.The first case shows that the combination of Mean Square Logarithmic Error(MSLE),ADAgrad,two layers for the auto-encoder,and ReLU had the best auto-encoder results with a Mean Absolute Error(MAE)=0.221 after 50 epochs and 75%classification with the best result for the classification algorithm.The second case shows the reflection of auto-encoder results on the classification results which is a combination ofMean Square Error(MSE),RMSprop,three layers for the auto-encoder,and ReLU,which had the best classification accuracy of 65%,the auto-encoder gives MAE=0.31 after 50 epochs.The third case is the worst,which is the combination of the hinge,RMSprop,three layers for the auto-encoder,and ReLU,providing accuracy of 20%and MAE=0.485.

Pluggable multitask diffractive neural networks based on cascaded metasurfaces

Optical neural networks have significant advantages in terms of power consumption,parallelism,and high computing speed,which has intrigued extensive attention in both academic and engineering communities.It has been considered as one of the powerful tools in promoting the fields of imaging processing and object recognition.However,the existing optical system architecture cannot be reconstructed to the realization of multi-functional artificial intelligence systems simultaneously.To push the development of this issue,we propose the pluggable diffractive neural networks(P-DNN),a general paradigm resorting to the cascaded metasurfaces,which can be applied to recognize various tasks by switching internal plug-ins.As the proof-of-principle,the recognition functions of six types of handwritten digits and six types of fashions are numerical simulated and experimental demonstrated at near-infrared regimes.Encouragingly,the proposed paradigm not only improves the flexibility of the optical neural networks but paves the new route for achieving high-speed,low-power and versatile artificial intelligence systems.

Social-ecological perspective on the suicidal behaviour factors of early adolescents in China:a network analysis

Background In early adolescence,youth are highly prone to suicidal behaviours.Identifying modifiable risk factors during this critical phase is a priority to inform effective suicide prevention strategies.Aims To explore the risk and protective factors of suicidal behaviours(ie,suicidal ideation,plans and attempts)in early adolescence in China using a social-ecological perspective.Methods Using data from the cross-sectional project‘Healthy and Risky Behaviours Among Middle School Students in Anhui Province,China',stratified random cluster sampling was used to select 5724 middle school students who had completed self-report questionnaires in November 2020.Network analysis was employed to examine the correlates of suicidal ideation,plans and attempts at four levels,namely individual(sex,academic performance,serious physical llness/disability,history of self-harm,depression,impulsivity,sleep problems,resilience),family(family economic status,relationship with mother,relationship with father,family violence,childhood abuse,parental mental illness),school(relationship with teachers,relationship with classmates,school-bullying victimisation and perpetration)and social(social support,satisfaction with society).Results In total,37.9%,19.0%and 5.5%of the students reported suicidal ideation,plans and attempts in the past 6 months,respectively.The estimated network revealed that suicidal ideation,plans and attempts were collectively associated with a history of self-harm,sleep problems,childhood abuse,school bullying and victimisation.Centrality analysis indicated that the most influential nodes in the network were history of self-harm and childhood abuse.Notably,the network also showed unique correlates of suicidal ideation(sex,weight=0.60;impulsivity,weight=0.24;family violence,weight=0.17;relationship with teachers,weight=-0.03;school-bullying perpetration,weight=0.22),suicidal plans(social support,weight=-0.15)and suicidal attempts(relationship with mother,weight=-0.10;parental mental llness,weight=0.61).Conclusions This study identified the correlates of suicidal ideation,plans and attempts,and provided practical implications for suicide prevention for young adolescents in China.Firstly,this study highlighted the importance of joint interventions across multiple departments.Secondly,the common risk factors of suicidal ideation,plans and attempts were elucidated.Thirdly,this study proposed target interventions to address the unique influencing factors of suicidal ideation,plans and attempts.

Image super‐resolution via dynamic network

Convolutional neural networks depend on deep network architectures to extract accurate information for image super‐resolution.However,obtained information of these con-volutional neural networks cannot completely express predicted high‐quality images for complex scenes.A dynamic network for image super‐resolution(DSRNet)is presented,which contains a residual enhancement block,wide enhancement block,feature refine-ment block and construction block.The residual enhancement block is composed of a residual enhanced architecture to facilitate hierarchical features for image super‐resolution.To enhance robustness of obtained super‐resolution model for complex scenes,a wide enhancement block achieves a dynamic architecture to learn more robust information to enhance applicability of an obtained super‐resolution model for varying scenes.To prevent interference of components in a wide enhancement block,a refine-ment block utilises a stacked architecture to accurately learn obtained features.Also,a residual learning operation is embedded in the refinement block to prevent long‐term dependency problem.Finally,a construction block is responsible for reconstructing high‐quality images.Designed heterogeneous architecture can not only facilitate richer structural information,but also be lightweight,which is suitable for mobile digital devices.Experimental results show that our method is more competitive in terms of performance,recovering time of image super‐resolution and complexity.The code of DSRNet can be obtained at https://github.com/hellloxiaotian/DSRNet.

Deep Learning-Based Stacked Auto-Encoder with Dynamic Differential Annealed Optimization for Skin Lesion Diagnosis

Intelligent diagnosis approaches with shallow architectural models play an essential role in healthcare.Deep Learning(DL)models with unsupervised learning concepts have been proposed because high-quality feature extraction and adequate labelled details significantly influence shallow models.On the other hand,skin lesionbased segregation and disintegration procedures play an essential role in earlier skin cancer detection.However,artefacts,an unclear boundary,poor contrast,and different lesion sizes make detection difficult.To address the issues in skin lesion diagnosis,this study creates the UDLS-DDOA model,an intelligent Unsupervised Deep Learning-based Stacked Auto-encoder(UDLS)optimized by Dynamic Differential Annealed Optimization(DDOA).Pre-processing,segregation,feature removal or separation,and disintegration are part of the proposed skin lesion diagnosis model.Pre-processing of skin lesion images occurs at the initial level for noise removal in the image using the Top hat filter and painting methodology.Following that,a Fuzzy C-Means(FCM)segregation procedure is performed using a Quasi-Oppositional Elephant Herd Optimization(QOEHO)algorithm.Besides,a novel feature extraction technique using the UDLS technique is applied where the parameter tuning takes place using DDOA.In the end,the disintegration procedure would be accomplished using a SoftMax(SM)classifier.The UDLS-DDOA model is tested against the International Skin Imaging Collaboration(ISIC)dataset,and the experimental results are examined using various computational attributes.The simulation results demonstrated that the UDLS-DDOA model outperformed the compared methods significantly.

Mapping Network-Coordinated Stacked Gated Recurrent Units for Turbulence Prediction

Accurately predicting fluid forces acting on the sur-face of a structure is crucial in engineering design.However,this task becomes particularly challenging in turbulent flow,due to the complex and irregular changes in the flow field.In this study,we propose a novel deep learning method,named mapping net-work-coordinated stacked gated recurrent units(MSU),for pre-dicting pressure on a circular cylinder from velocity data.Specifi-cally,our coordinated learning strategy is designed to extract the most critical velocity point for prediction,a process that has not been explored before.In our experiments,MSU extracts one point from a velocity field containing 121 points and utilizes this point to accurately predict 100 pressure points on the cylinder.This method significantly reduces the workload of data measure-ment in practical engineering applications.Our experimental results demonstrate that MSU predictions are highly similar to the real turbulent data in both spatio-temporal and individual aspects.Furthermore,the comparison results show that MSU predicts more precise results,even outperforming models that use all velocity field points.Compared with state-of-the-art methods,MSU has an average improvement of more than 45%in various indicators such as root mean square error(RMSE).Through comprehensive and authoritative physical verification,we estab-lished that MSU’s prediction results closely align with pressure field data obtained in real turbulence fields.This confirmation underscores the considerable potential of MSU for practical applications in real engineering scenarios.The code is available at https://github.com/zhangzm0128/MSU.

Activation Redistribution Based Hybrid Asymmetric Quantization Method of Neural Networks

The demand for adopting neural networks in resource-constrained embedded devices is continuously increasing.Quantization is one of the most promising solutions to reduce computational cost and memory storage on embedded devices.In order to reduce the complexity and overhead of deploying neural networks on Integeronly hardware,most current quantization methods use a symmetric quantization mapping strategy to quantize a floating-point neural network into an integer network.However,although symmetric quantization has the advantage of easier implementation,it is sub-optimal for cases where the range could be skewed and not symmetric.This often comes at the cost of lower accuracy.This paper proposed an activation redistribution-based hybrid asymmetric quantizationmethod for neural networks.The proposedmethod takes data distribution into consideration and can resolve the contradiction between the quantization accuracy and the ease of implementation,balance the trade-off between clipping range and quantization resolution,and thus improve the accuracy of the quantized neural network.The experimental results indicate that the accuracy of the proposed method is 2.02%and 5.52%higher than the traditional symmetric quantization method for classification and detection tasks,respectively.The proposed method paves the way for computationally intensive neural network models to be deployed on devices with limited computing resources.Codes will be available on https://github.com/ycjcy/Hybrid-Asymmetric-Quantization.

The optimal atropine concentration for myopia control in Chinese children: a systematic review and network Metaanalysis

AIM:To figure out whether various atropine dosages may slow the progression of myopia in Chinese kids and teenagers and to determine the optimal atropine concentration for effectively slowing the progression of myopia.METHODS:A systematic search was conducted across the Cochrane Library,PubMed,Web of Science,EMBASE,CNKI,CBM,VIP,and Wanfang database,encompassing literature on slowing progression of myopia with varying atropine concentrations from database inception to January 17,2024.Data extraction and quality assessment were performed,and a network Meta-analysis was executed using Stata version 14.0 Software.Results were visually represented through graphs.RESULTS:Fourteen papers comprising 2475 cases were included;five different concentrations of atropine solution were used.The network Meta-analysis,along with the surface under the cumulative ranking curve(SUCRA),showed that 1%atropine(100%)>0.05%atropine(74.9%)>0.025%atropine(51.6%)>0.02%atropine(47.9%)>0.01%atropine(25.6%)>control in refraction change and 1%atropine(98.7%)>0.05%atropine(70.4%)>0.02%atropine(61.4%)>0.025%atropine(42%)>0.01%atropine(27.4%)>control in axial length(AL)change.CONCLUSION:In Chinese children and teenagers,the five various concentrations of atropine can reduce the progression of myopia.Although the network Meta-analysis showed that 1%atropine is the best one for controlling refraction and AL change,there is a high incidence of adverse effects with the use of 1%atropine.Therefore,we suggest that 0.05%atropine is optimal for Chinese children to slow myopia progression.

Rao Algorithms-Based Structure Optimization for Heterogeneous Wireless Sensor Networks

The structural optimization of wireless sensor networks is a critical issue because it impacts energy consumption and hence the network’s lifetime.Many studies have been conducted for homogeneous networks,but few have been performed for heterogeneouswireless sensor networks.This paper utilizes Rao algorithms to optimize the structure of heterogeneous wireless sensor networks according to node locations and their initial energies.The proposed algorithms lack algorithm-specific parameters and metaphorical connotations.The proposed algorithms examine the search space based on the relations of the population with the best,worst,and randomly assigned solutions.The proposed algorithms can be evaluated using any routing protocol,however,we have chosen the well-known routing protocols in the literature:Low Energy Adaptive Clustering Hierarchy(LEACH),Power-Efficient Gathering in Sensor Information Systems(PEAGSIS),Partitioned-based Energy-efficient LEACH(PE-LEACH),and the Power-Efficient Gathering in Sensor Information Systems Neural Network(PEAGSIS-NN)recent routing protocol.We compare our optimized method with the Jaya,the Particle Swarm Optimization-based Energy Efficient Clustering(PSO-EEC)protocol,and the hybrid Harmony Search Algorithm and PSO(HSA-PSO)algorithms.The efficiencies of our proposed algorithms are evaluated by conducting experiments in terms of the network lifetime(first dead node,half dead nodes,and last dead node),energy consumption,packets to cluster head,and packets to the base station.The experimental results were compared with those obtained using the Jaya optimization algorithm.The proposed algorithms exhibited the best performance.The proposed approach successfully prolongs the network lifetime by 71% for the PEAGSIS protocol,51% for the LEACH protocol,10% for the PE-LEACH protocol,and 73% for the PEGSIS-NN protocol;Moreover,it enhances other criteria such as energy conservation,fitness convergence,packets to cluster head,and packets to the base station.

Biodiversity metrics on ecological networks: Demonstrated with animal gastrointestinal microbiomes

Biodiversity has become a terminology familiar to virtually every citizen in modern societies.It is said that ecology studies the economy of nature,and economy studies the ecology of humans;then measuring biodiversity should be similar with measuring national wealth.Indeed,there have been many parallels between ecology and economics,actually beyond analogies.For example,arguably the second most widely used biodiversity metric,Simpson(1949)’s diversity index,is a function of familiar Gini-index in economics.One of the biggest challenges has been the high“diversity”of diversity indexes due to their excessive“speciation”-there are so many indexes,similar to each country’s sovereign currency-leaving confused diversity practitioners in dilemma.In 1973,Hill introduced the concept of“numbers equivalent”,which is based on Renyi entropy and originated in economics,but possibly due to his abstruse interpretation of the concept,his message was not widely received by ecologists until nearly four decades later.What Hill suggested was similar to link the US dollar to gold at the rate of$35 per ounce under the Bretton Woods system.The Hill numbers now are considered most appropriate biodiversity metrics system,unifying Shannon,Simpson and other diversity indexes.Here,we approach to another paradigmatic shift-measuring biodiversity on ecological networks-demonstrated with animal gastrointestinal microbiomes representing four major invertebrate classes and all six vertebrate classes.The network diversity can reveal the diversity of species interactions,which is a necessary step for understanding the spatial and temporal structures and dynamics of biodiversity across environmental gradients.

Falcon Optimization Algorithm-Based Energy Efficient Communication Protocol for Cluster-Based Vehicular Networks

Rapid development in Information Technology(IT)has allowed several novel application regions like large outdoor vehicular networks for Vehicle-to-Vehicle(V2V)transmission.Vehicular networks give a safe and more effective driving experience by presenting time-sensitive and location-aware data.The communication occurs directly between V2V and Base Station(BS)units such as the Road Side Unit(RSU),named as a Vehicle to Infrastructure(V2I).However,the frequent topology alterations in VANETs generate several problems with data transmission as the vehicle velocity differs with time.Therefore,the scheme of an effectual routing protocol for reliable and stable communications is significant.Current research demonstrates that clustering is an intelligent method for effectual routing in a mobile environment.Therefore,this article presents a Falcon Optimization Algorithm-based Energy Efficient Communication Protocol for Cluster-based Routing(FOA-EECPCR)technique in VANETS.The FOA-EECPCR technique intends to group the vehicles and determine the shortest route in the VANET.To accomplish this,the FOA-EECPCR technique initially clusters the vehicles using FOA with fitness functions comprising energy,distance,and trust level.For the routing process,the Sparrow Search Algorithm(SSA)is derived with a fitness function that encompasses two variables,namely,energy and distance.A series of experiments have been conducted to exhibit the enhanced performance of the FOA-EECPCR method.The experimental outcomes demonstrate the enhanced performance of the FOA-EECPCR approach over other current methods.

Multi-Scale-Matching neural networks for thin plate bending problem

Physics-informed neural networks are a useful machine learning method for solving differential equations,but encounter challenges in effectively learning thin boundary layers within singular perturbation problems.To resolve this issue,multi-scale-matching neural networks are proposed to solve the singular perturbation problems.Inspired by matched asymptotic expansions,the solution is decomposed into inner solutions for small scales and outer solutions for large scales,corresponding to boundary layers and outer regions,respectively.Moreover,to conform neural networks,we introduce exponential stretched variables in the boundary layers to avoid semiinfinite region problems.Numerical results for the thin plate problem validate the proposed method.

Correcting Climate Model Sea Surface Temperature Simulations with Generative Adversarial Networks:Climatology,Interannual Variability,and Extremes

Climate models are vital for understanding and projecting global climate change and its associated impacts.However,these models suffer from biases that limit their accuracy in historical simulations and the trustworthiness of future projections.Addressing these challenges requires addressing internal variability,hindering the direct alignment between model simulations and observations,and thwarting conventional supervised learning methods.Here,we employ an unsupervised Cycle-consistent Generative Adversarial Network(CycleGAN),to correct daily Sea Surface Temperature(SST)simulations from the Community Earth System Model 2(CESM2).Our results reveal that the CycleGAN not only corrects climatological biases but also improves the simulation of major dynamic modes including the El Niño-Southern Oscillation(ENSO)and the Indian Ocean Dipole mode,as well as SST extremes.Notably,it substantially corrects climatological SST biases,decreasing the globally averaged Root-Mean-Square Error(RMSE)by 58%.Intriguingly,the CycleGAN effectively addresses the well-known excessive westward bias in ENSO SST anomalies,a common issue in climate models that traditional methods,like quantile mapping,struggle to rectify.Additionally,it substantially improves the simulation of SST extremes,raising the pattern correlation coefficient(PCC)from 0.56 to 0.88 and lowering the RMSE from 0.5 to 0.32.This enhancement is attributed to better representations of interannual,intraseasonal,and synoptic scales variabilities.Our study offers a novel approach to correct global SST simulations and underscores its effectiveness across different time scales and primary dynamical modes.

Method of Multi-Mode Sensor Data Fusion with an Adaptive Deep Coupling Convolutional Auto-Encoder

To address the difficulties in fusing multi-mode sensor data for complex industrial machinery, an adaptive deep coupling convolutional auto-encoder (ADCCAE) fusion method was proposed. First, the multi-mode features extracted synchronously by the CCAE were stacked and fed to the multi-channel convolution layers for fusion. Then, the fused data was passed to all connection layers for compression and fed to the Softmax module for classification. Finally, the coupling loss function coefficients and the network parameters were optimized through an adaptive approach using the gray wolf optimization (GWO) algorithm. Experimental comparisons showed that the proposed ADCCAE fusion model was superior to existing models for multi-mode data fusion.

Unraveling the Fundamental Mechanism of Interface Conductive Network Influence on the Fast‑Charging Performance of SiO‑Based Anode for Lithium‑Ion Batteries

Progress in the fast charging of high-capacity silicon monoxide(SiO)-based anode is currently hindered by insufficient conductivity and notable volume expansion.The construction of an interface conductive network effectively addresses the aforementioned problems;however,the impact of its quality on lithium-ion transfer and structure durability is yet to be explored.Herein,the influence of an interface conductive network on ionic transport and mechanical stability under fast charging is explored for the first time.2D modeling simulation and Cryo-transmission electron microscopy precisely reveal the mitigation of interface polarization owing to a higher fraction of conductive inorganic species formation in bilayer solid electrolyte interphase is mainly responsible for a linear decrease in ionic diffusion energy barrier.Furthermore,atomic force microscopy and Raman shift exhibit substantial stress dissipation generated by a complete conductive network,which is critical to the linear reduction of electrode residual stress.This study provides insights into the rational design of optimized interface SiO-based anodes with reinforced fast-charging performance.

Multi-scale physics-informed neural networks for solving high Reynolds number boundary layer flows based on matched asymptotic expansions

Multi-scale system remains a classical scientific problem in fluid dynamics,biology,etc.In the present study,a scheme of multi-scale Physics-informed neural networks is proposed to solve the boundary layer flow at high Reynolds numbers without any data.The flow is divided into several regions with different scales based on Prandtl's boundary theory.Different regions are solved with governing equations in different scales.The method of matched asymptotic expansions is used to make the flow field continuously.A flow on a semi infinite flat plate at a high Reynolds number is considered a multi-scale problem because the boundary layer scale is much smaller than the outer flow scale.The results are compared with the reference numerical solutions,which show that the msPINNs can solve the multi-scale problem of the boundary layer in high Reynolds number flows.This scheme can be developed for more multi-scale problems in the future.